There are 39 left handed students at Toms school
To simplify this expression, first you would have to distribute the negative or subtraction throughout the second group of parentheses.
After we do this, we get the simplified expression:
ab + 8a + 1 + 6ab - 4
Now, we must simplify like terms, meaning combine the terms that have the same variable.
7ab + 8a - 3
That is your final answer ^^^
Answer:
A) Verified
B) Proved
Step-by-step explanation:
a) Let's verify it for 2 x 2 matrix,
![A=\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da%26b%5C%5Cc%26d%5Cend%7Barray%7D%5Cright%5D)
and ![B=\left[\begin{array}{ccc}e&f\\g&h\end{array}\right]](https://tex.z-dn.net/?f=B%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7De%26f%5C%5Cg%26h%5Cend%7Barray%7D%5Cright%5D)
![AB=\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]\left[\begin{array}{ccc}e&f\\g&h\end{array}\right]=\left[\begin{array}{ccc}a.e+b.g&a.f+b.h\\c.e+d.g&c.f+d.h\end{array}\right]](https://tex.z-dn.net/?f=AB%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da%26b%5C%5Cc%26d%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7De%26f%5C%5Cg%26h%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da.e%2Bb.g%26a.f%2Bb.h%5C%5Cc.e%2Bd.g%26c.f%2Bd.h%5Cend%7Barray%7D%5Cright%5D)
![(AB)^{-1}=\frac{1}{(a.e+b.g)(c.f+d.h)-(a.f+b.h)(c.e+d.g)}\left[\begin{array}{ccc}c.f+d.h&-(a.f+b.h)\\-(c.e+d.g)&a.e+b.g\end{array}\right]](https://tex.z-dn.net/?f=%28AB%29%5E%7B-1%7D%3D%5Cfrac%7B1%7D%7B%28a.e%2Bb.g%29%28c.f%2Bd.h%29-%28a.f%2Bb.h%29%28c.e%2Bd.g%29%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dc.f%2Bd.h%26-%28a.f%2Bb.h%29%5C%5C-%28c.e%2Bd.g%29%26a.e%2Bb.g%5Cend%7Barray%7D%5Cright%5D)
![A^{-1}=\frac{1}{a.d-b.c} \left[\begin{array}{ccc}d&-b\\-c&a\end{array}\right]](https://tex.z-dn.net/?f=A%5E%7B-1%7D%3D%5Cfrac%7B1%7D%7Ba.d-b.c%7D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dd%26-b%5C%5C-c%26a%5Cend%7Barray%7D%5Cright%5D)
![B^{-1}=\frac{1}{e.h-f.g} \left[\begin{array}{ccc}h&-f\\-g&e\end{array}\right]](https://tex.z-dn.net/?f=B%5E%7B-1%7D%3D%5Cfrac%7B1%7D%7Be.h-f.g%7D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dh%26-f%5C%5C-g%26e%5Cend%7Barray%7D%5Cright%5D)
![B^{-1}A^{-1}=\frac{1}{(a.e+b.g)(c.f+d.h)-(a.f+b.h)(c.e+d.g)}\left[\begin{array}{ccc}c.f+d.h&-(a.f+b.h)\\-(c.e+d.g)&a.e+b.g\end{array}\right]](https://tex.z-dn.net/?f=B%5E%7B-1%7DA%5E%7B-1%7D%3D%5Cfrac%7B1%7D%7B%28a.e%2Bb.g%29%28c.f%2Bd.h%29-%28a.f%2Bb.h%29%28c.e%2Bd.g%29%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dc.f%2Bd.h%26-%28a.f%2Bb.h%29%5C%5C-%28c.e%2Bd.g%29%26a.e%2Bb.g%5Cend%7Barray%7D%5Cright%5D)
So it is proved that the results are same.
b) Now, let's prove it for any n x n matrix.
Answer:
y = (-6/7)x - 1
Step-by-step explanation:
There's a dot where this line crosses the y-axis; it's represented by the point (0, -1). Consequently, the y-intercept, b, of this line is -1.
As x increases from -6 to 0, y decreases from 7 to -1. The change in x is 7 units and the change in y is -6 units. Thus, the slope of this line is
m = rise / run = -6 / 7.
Again, the y-intercept is b = -1.
Thus, inserting the knowns into the slope-intercept form of the equation of a straight line results in:
y = (-6/7)x - 1
Answer:
Step-by-step explanation:
The dot on -4 is hollow, so that is just the regular less than sign. (<)
The dot on the 5 is filled in, so that is the equal to or less than sign. (≤)
